Fast calculation of the electrostatic potential in ionic crystals by direct summation method

Abstract

An efficient real space method is derived for the evaluation of the Madelung's potential of ionic crystals. The proposed method is an extension of the Evjen's method. It takes advantage of a general analysis for the potential convergence in real space. Indeed, we show that the series convergence is exponential as a function of the number of annulled multipolar momenta in the unit cell. The method proposed in this work reaches such an exponential convergence rate. Its efficiency is comparable to the Ewald's method, however unlike the latter, it uses only simple algebraic functions.

Cited by in corpus (9)

• Intervalence Charge Transfer Luminescence: Interplay between anomalous and 5d-4f emissions in Yb-doped fluorite-type crystals
• Intervalence Charge Transfer luminescence: The anomalous luminescence of Cerium-doped Cs2LiLuCl6 elpasolite
• Electronic structure of the $\mathrm{C}{\mathrm{a}}_3\mathrm{C}{\mathrm{o}}_4{\mathrm{O}}_9$ compound from ab initio local interactions
• An ab initio study of magneto-electric coupling of $\mathrm{YMn}{\mathrm{O}}_3$
• Accurate evaluation of magnetic coupling between atoms with numerous open-shells : an ab-initio method
• Real-space fluctuations of effective exchange integrals in high-Tc cuprates
• The Madelung Constant in $N$ Dimensions
• The Finite Coulomb Lattice Sum: A Resolution of Conditional Convergence through Exact Shape and Size
• Analytic Boundary Terms for Arbitrary Crystal Geometries and Direct-Sum Evaluation of Madelung Constants in Triclinic Lattices